The Lagrangian Mechanics and Pseudo-Periodicity of The Many-Body Planar Pendulum System

TL;DR

This paper derives the equations of motion for a system of coupled planar pendulums, analyzes their pseudo-periodicity as the number of pendulums varies, and validates the model through numerical simulations.

Contribution

It introduces a linearized idealized model for the pseudo-periodicity of many-body pendulum systems and validates it with numerical data.

Findings

Pseudo-periodicity depends on the number of pendulums N

Model aligns well with numerical simulation results

Provides a framework for analyzing complex coupled pendulum systems

Abstract

We present the Euler--Langrage equations for a many-body system of coupled planar pendulums. Hence, imposing initial condition data, the equations of motion are linearized and later developed in an idealized model for the pseudo-periodicity of the system as a function of the number of pendulums $N$. The result is empirically corroborated by comparing the model with data obtained via a numerical simulation, and by employing Kane's Method integrator in Python.